Question

If two equal chords AB and CD of a circle intersect within the circle , prove that AD=BC.​

Answer 1

Answer:

From the figure there are two triangles ΔAED and ΔCEB

To prove ΔAED and ΔCEB

From the figure we get,

<AED=<CEB(Vertically opposite angles are equal)

<A=<C(since <A and <C are on the angle subtended on the same arc)

Similarly <D=<B

All angle are equal. Therefore ΔAED≅ΔCEB

To prove AD=CB

Since ΔAED≅ΔCEB

ByCPCT(Corresponding parts of congruent triangles)

AE=CE,ED=EB and AD=BC

HENCE PROVED